Thanks to recent advances in electron microscope instrumentation [1]}, [2]}, [3]} that enable electron energy-loss spectroscopy (EELS) to be performed with few-meV spectral resolution [2]}, [3]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, free electron beams (e-beams) allow us to map the atomic structure of materials with sub-Ångstrom spatial resolution [16]}, while additionally granting us access into the atomic-scale properties of electronic and phononic excitations at frequencies extending down to the mid-infrared. When the electrons are extracted from a photocathode, simultaneous exposure of the specimen to synchronized laser and electron pulses trigger ultrafast interactions that can be used to shape [17]}, [18]}, [19]}, [20]} and compress [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]} the electron wave function along directions parallel [19]}, [31]}, [32]}, [33]}, [34]}, [35]} and transverse [36]}, [37]}, [38]}, [39]} with respect to the e-beam. Such interactions have also been investigated as a way to map the temporal evolution of optical excitations in the so-called photon-induced near-field electron microscopy (PINEM) [19]}, [31]}, [32]}, [43]}, [44]}, [33]}, [34]}, [47]}, [35]}, [49]}, [50]}, [51]}, [52]}, [23]}, [54]}, [55]}, [56]}, [36]}, [37]}, [59]}, [38]}, [61]}, [62]}, [63]}, [64]}, [65]}, [66]}, [67]}, [68]}, [69]}, [70]}, [71]}, [72]}, [73]} technique, which has been applied, for example, to image the femtosecond dynamics of plasmon [33]}, [47]} and phonon-polariton [72]} optical fields. These studies have focused on optical excitations of bosonic nature, in which the materials respond linearly to the fields associated with both light and electrons, while the activation of nonlinear sample response driven by intense laser illumination can affect the electron spectra, potentially enabling the measurement of nonlinear response functions with nanoscale spatial resolution [77]}.
